scholarly journals Disordered loops in the two-dimensional antiferromagnetic spin–fermion model

2008 ◽  
Vol 795 (3) ◽  
pp. 578-595
Author(s):  
T. Enss ◽  
S. Caprara ◽  
C. Castellani ◽  
C. Di Castro ◽  
M. Grilli
Keyword(s):  
Two Dimensional ◽  
Fermion Model ◽  
Antiferromagnetic Spin

THE SIMULATION OF 2D SPIN-1 ISING MODEL WITH POSITIVE BIQUADRATIC INTERACTION ON A CELLULAR AUTOMATON

2003 ◽  
Vol 14 (10) ◽  
pp. 1305-1320 ◽  
Author(s):  
BÜLENT KUTLU
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Cellular Automaton ◽  
Intermediate Phase ◽  
Finite Size ◽  
Square Lattice ◽  
Two Dimensional ◽  
Finite Size Scaling ◽  
Creutz Cellular Automaton ◽  
Antiferromagnetic Spin

The two-dimensional antiferromagnetic spin-1 Ising model with positive biquadratic interaction is simulated on a cellular automaton which based on the Creutz cellular automaton for square lattice. Phase diagrams characterizing phase transition of the model are presented for a comparison with those obtained from other calculations. We confirm the existence of the intermediate phase observed in previous works for some values of J/K and D/K. The values of the static critical exponents (β, γ and ν) are estimated within the framework of the finite-size scaling theory for D/K<2J/K. Although the results are compatible with the universal Ising critical behavior in the region of D/K<2J/K-4, the model does not exhibit any universal behavior in the interval 2J/K-4<D/K<2J/K.

scholarly journals Calculation of the Exchange Constant in 2D Wigner Liquid

1999 ◽  
Vol 52 (5) ◽  
pp. 845
Author(s):  
V. V. Flambaum ◽  
I. V. Ponomarev ◽  
O. P. Sushkov
Keyword(s):  
Magnetic Order ◽  
Recent Observation ◽  
Metallic Phase ◽  
Range Order ◽  
Spin Interaction ◽  
Exchange Constant ◽  
Two Dimensional ◽  
Metal Insulator ◽  
Theoretical Question ◽  
Antiferromagnetic Spin

The recent observation of a two-dimensional (2D) metal–insulator transition in semiconductor devices and the strong influence of a magnetic field on the metallic phase has attracted a great deal of interest. This gives rise to the important theoretical question about the nature and the magnetic order of insulating and conducting phases. In the present paper we calculate (both analytically and numerically) the exchange constant for a two-dimensional Wigner liquid— the state with destroyed long-range order but preserved short-range order. It is demonstrated that there is an antiferromagnetic spin–spin interaction between nearest electrons. We also discuss a possible pairing of the electrons in a 2D Wigner crystal by the spin-Peierls mechanism.

Local three-spin correlations in the free-fermion and planar Ising models

1989 ◽  
Vol 423 (1865) ◽  
pp. 279-300 ◽  
Keyword(s):  
Ising Model ◽  
Ising Models ◽  
Square Lattice ◽  
Free Fermion ◽  
Two Dimensional ◽  
Solvable Models ◽  
Spin Correlations ◽  
Fermion Model ◽  
Free Fermion Model

A number of local three-spin correlations are calculated exactly for various related ferromagnetic two-dimensional solvable models in statistical mechanics.They are the square lattice free-fermion model, the equivalent checkerboard Ising model, and the anisotropic triangular, honeycomb and square lattice Ising models. The different results are all applications of a single unifying formula.

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